Â¬â€  Â¬â€  Â¬â€  Â¬â€  Â¬â€

# COMPLEX

Section: Linux Programmer's Manual (7)
Updated: 2002-07-28
Index Return to Main Contents

## NAME

complex - basics of complex mathematics

## SYNOPSIS

#include <complex.h>

## DESCRIPTION

Complex numbers are numbers of the form z = a+b*i, where a and b are real numbers and i = sqrt(-1), so that i*i = -1.
There are other ways to represent that number. The pair (a,b) of real numbers may be viewed as a point in the plane, given by X- and Y-coordinates. This same point may also be described by giving the pair of real numbers (r,phi), where r is the distance to the origin O, and phi the angle between the X-axis and the line Oz. Now z = r*exp(i*phi) = r*(cos(phi)+i*sin(phi)).

The basic operations are defined on z = a+b*i and w = c+d*i as:

addition: z+w = (a+c) + (b+d)*i
multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i
division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i

Nearly all math function have a complex counterpart but there are some complex-only functions.

## EXAMPLE

Your C-compiler can work with complex numbers if it supports the C99 standard. Link with -lm. The imaginary unit is represented by I.

```/* check that exp(i * pi) == -1 */
#include <math.h>        /* for atan */
#include <complex.h>

int
main(void)
{
double pi = 4 * atan(1.0);
complex z = cexp(I * pi);
printf("%f + %f * i\n", creal(z), cimag(z));
}
```

## SEE ALSO

cabs(3), carg(3), cexp(3), cimag(3), creal(3)

## COLOPHON

This page is part of release 3.21 of the Linux man-pages project. A description of the project, and information about reporting bugs, can be found at http://www.kernel.org/doc/man-pages/.

NAME
SYNOPSIS
DESCRIPTION
EXAMPLE
SEE ALSO
COLOPHON

# Administrator

## Comments

Subscribe to Comments Feed

### Upcoming Linux Foundation Courses

1. LFS220 Linux System Administration
30 Nov » 03 Dec - Virtual
2. LFS416 Linux Security
07 Dec » 10 Dec - Virtual
3. LFD411 Embedded Linux Development
07 Dec » 11 Dec - Atlanta

View All Upcoming Courses

## Sign Up For the Linux.com Newsletter

### Who we are ?

The Linux Foundation is a non-profit consortium dedicated to the growth of Linux.

More About the foundation...

Frequent Questions

Answers

Blogs

Forums